The earliest example of a gear train dates to at least 2,000 B.C. when Chinese engineers built a chariot that used a complex planetary mechanism made of wooden gears to let a dragon head continuously point south when driven around (Ref. 1). In Greece, a surprisingly advanced Antikythera gearbox mechanism, incorporating at least 37 precisely crafted bronze gears, was built years later, between 205–60 B.C. (Ref. 2).

Today, gearboxes are inevitable in numerous applications requiring high power density including wind turbines, electric vehicles, cranes, robotics, etc. A combination of high-ratio gearboxes with high-speed, low-torque motors is often used to achieve high power density. Planetary gear trains (PGTs) help achieve a high gear ratio in a compact arrangement. Several configurations of planetary gears are widely studied in this article where the gear profiles used in these studies are primarily involute.